I think the danger here is far smaller than people are making it out to be. There is a major difference between the label "rationalist" and most other identities as Paul Graham refers to them. The difference is that "rationalist" is a procedural label; most identities are at least partially substantive, using procedural/substantive in the sense that the legal system does.

"Rationalist," which I agree is an inevitable shorthand that emerges when the topic of overcoming bias is discussed frequently, is exclusively a procedural label: such a person is expected to make decisions and seek truth using a certain process. This process includes Bayesian updating of priors based on evidence, etc. However, such a label doesn't commit the rationalist to any particular conclusion ex ante: the rationalist doesn't have to be atheist or theist, or accept any other fact as true and virtually unassailable. He's merely committed to the process of arriving at conclusions.

Other identities are largely substantive. They commit the bearer to certain conclusions about the state of the world. A Christian believes in a god with certain attributes and a certain history of the world. A Communist believes that a certain government system is better than all others. These identities are dangerous: once they commit you to a conclusion, you're unlikely to challenge it with evidence to ensure it is in fact the best one. That's the kind of identity Paul Graham is warning against.

Of course, these labels have procedural components: a Christian would solve a moral dilemma using the Bible; a Communist would solve an economic problem using communist theory. Similarly, rationalism substantively means you've arrived at the conclusion than you're biased and you can't trust your gut or your brain like most people do, but that's the extent of your substantive assumptions.

Since rationalism is a procedural identity rather than a substantive one, I see few of the dangers of using the term "rationalist" freely here.